Physics, 29.11.2019 00:31 mirmir62

Hoover dam on the colorado river is the highest dam in the united states at 221m, with a power output of 680 mw. the dam generates electricity by flowing water down to a point 150 m below the stop, at an average flow rate of 650 m3/s.
part (a) calculate the power in this flow in watts.

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Answer from: jakester00792

Power = 9.75 ×10^8 $\frac{kgm^2}{s^3}$

Explanation:

Power is rate of change of energy.Here gravitational energy is transferred to kinetic energy of water at a definite rate.

For one second 650m^3 of water flows out down to 150m oh depth.

So, the energy at a height of 150m is transformed to kinetic energy.

for a second,

650m^3 of water flows down ⇒ (1000kg/m^3 × 650m^3) = 6.5×10^5kg of warer flos down.

The total gravitational potential energy stored in water is

= mass of water × height× gravity

= 6.5 ×10^5 × 150 × 10 = 9.75 ×10^8 $\frac{kgm^2}{s^2}$

As it is transformed in a second it is also equal to Power.

Answer from: khenalilovespandas

power = 1407.77 MW

Explanation:

The basic principle of a hydro electric station is the conversion of potential energy to electrical energy. Here, water is allowed to fall from a height which will increase its the kinetic energy. This high speed flowing water is used to rotate the shaft of a turbine which will in turn produce electrical energy.

So here,

power = rate of change of potential energy with respect to time

power = $\frac{d(mgh)}{dt}$

where,

m = mass of water

g = acceleration due to gravity

h = height through which the water falls

here h and g are constants ( h is the total height through which the water falls and it doesn't change with time). Therefore we can take them out of differentiation.

thus,

power = gh $\frac{d(m)}{dt}$

now,

m = ρV

where,

ρ = density

V = volume

substituting this in the above equation we get,

power = gh $\frac{d(ρV)}{dt}$

again ρ is a constant. Thus,

power = ρgh $\frac{d(V)}{dt}$

Given that,

h = 221 m

$\frac{d(V)}{dt}$ = 650 $m^{3}$ /s

g = 9.8 m/ $s^{2}$

ρ = 1000 kg/ $m^{3}$

substituting these values in the above equation

power = 1000 x 9.8 x 221 x 650

power = 1407.77 MW

Answer from: Quest

distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

slope of a graph = change in value of y -axis / change in values of x -axis

comparing both the equations

change in value of y -axis = change in position

change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.

Answer from: Quest

this would be about 43%

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Hoover dam on the colorado river is the highest dam in the united states at 221m, with a power outpu...

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